Constructions of Flexible-Size Deterministic Measurement Matrices Using Protograph LDPC Codes and Hadamard Codes

In this letter, we conduct an insightful study on protograph-low-density parity-check (PLDPC)-code-assisted deterministic measurement matrices for compressed sensing applications. As is well known, the recovery performance of conventional PLDPC sparse matrices (PLDPC-SM) will be dramatically degraded as the ratio of N to M increases, where M x N is the size of the matrices. To address the above issue, we propose a novel construction method to formulate a class of extended PLDPC-SM (EPLDPC-SM) by intelligently inserting part of Hadamard matrices into the conventional PLDPC-SM. The proposed EPLDPC-SM not only can realize more flexible sizes with respect to the existing counterparts, but also can be amenable to lower coherence without costing more storage resources. Both coherence analyses and experiment results demonstrate that the proposed EPLDPC-SM are superior to the well-performing deterministic measurement matrices (i.e., PLDPC-SM) and random matrices (i.e., random Gaussian matrices (R-GM) and random sparse matrices (R-SBM)) for various values of N/M.(1)